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NASA NTRS1982

In-plane inertial coupling in tuned and severely mistuned bladed disks

A model has been developed and verified for blade-disk-shaft coupling in rotors due to the in-plane rigid body modes of the disk. An analytic model has been developed which couples the in-plane rigid body modes of the disk on an elastic shaft with the blade bending modes. Bench resonance test were carried out on the M.I.T. Compressor Rotor, typical of research rotors with flexible blades and a thick rigid disk. When the rotor was carefully tuned, the structural coupling of the blades by the disks was confined to zero and one nodal diameter modes, whose modal frequencies were greater than the blade cantilever frequency. In the case of the tuned rotor, and in two cases where severe mistuning was intentionally introduced, agreement between the predicted and observed natural frequencies is excellent. The analytic model was then extended to include the effects of constant angular rotation of the disk.

Crawley, E. F.↗

NASA NTRS1983

Stability experiments in rotating-disk flow

An experimental study of the transitional flow on a flat disk, rotating in still air, has been conducted. Using digitized hot-wire data, the axes of the stationary spiral vortices, which are the primary instability mechanism for the disk flow, have been mapped-out in terms of both spatial coordinates and velocity fluctuations. Data are presented for a clean disk and for a disk with a single, isolated roughness element. The data show that the disk vortices are generated at discrete roughness disturbance sites on the disk and that they propagate and grow as wave packets. The familiar vortex pattern of 30 or so vortices results only when these wave packets have merged and filled the entire circumference. The appearance of stationary, secondary vortices prior to turbulent breakdown has also been observed. Comparisons with linear stability theory show reasonable agreement with measured growth rate data.

Wilkinson, S. P.↗

NASA NTRS1984

Black hole accretion disks - Coronal stabilization of the Lightman-Eardley instability

Physical processes by which the presence of a corona around a black hole can raise the threshold of onset of the Lightman-Eardley (L-E, 1976) instability are explored analytically. The L-E model predicts that an optically thick disk becomes unstable when the disk radiation pressure exceeds the disk gas pressure. The model has important implications for the validity of either the coronal disk or two-temperature disk models for accretion zones around black holes. It is shown that a corona can dissipate accreting gravitational energy through radiative cooling. Specific ratios of hard/soft X-rays are quantified for stable and unstable conditions. X-ray spectra from Cyg X-1 are cited as residing below the instability threshold value and thus are supportive of the coronal disk model.

Ionson, J. A.↗

NASA NTRS1985

Self-regulating galaxy formation. I - H II disk and Lyman-alpha pressure

The nascent interstellar medium and star formation model are incorporated into a scenario for the formation epoch of spiral galaxies. The structure, star formation time scale, and luminosity of a self-gravitating isothermal disk are evaluated as functions of the disk surface density. The importance of radiation pressure, particularly that of Lyman-alpha, in maintaining an inflated disk and halting infall is discussed. The Lyman-alpha pressure also supports a considerable halo of material in the vicinity of the disk. A first-order infall scenario and the time-dependent properties of the system it constructs are presented. Disk properties are evaluated at the epoch at which further material is supportable against infall by Lyman-alpha pressure. The two-dimensional family of disk galaxies whose scales and surface density are expressible in terms of fundamental constants and which arise from the three parameter sets of perturbations in the Hubble flow are determined.

Cox, D. P.↗

NASA NTRS1987

Generation of a dynamo magnetic field in a protoplanetary accretion disk

A new computational technique is developed that allows realistic calculations of dynamo magnetic field generation in disk geometries corresponding to protoplanetary and protostellar accretion disks. The approach is of sufficient generality to allow, in the future, a wide class of accretion disk problems to be solved. Here, basic modes of a disk dynamo are calculated. Spatially localized oscillatory states are found to occur in Keplerain disks. A physical interpretation is given that argues that spatially localized fields of the type found in these calculations constitute the basic modes of a Keplerian disk dynamo.

Stepinski, T.↗

NASA NTRS1987

Constraints on quasar accretion disks from the optical/ultraviolet/soft X-ray big bump

The simplest accretion-disk models have difficulties explaining the optical/UV/soft-X-ray 'big bump' in quasars. Here more realistic models are investigated, incorporating opacity and inclination effects while retaining an analytic form for ease of computation. It is found that opacity effects can explain the uniform 20,000-30,000 K 'maximum disk temperature' derived by previous workers. The observed spectral turndown would be the result of the onset of electron scattering and should not be identified with the hottest part of the disk. The frequency at which this spectral turndown occurs is only weakly dependent on the accretion-disk parameters. These opacity effects also allow high-frequency EUV and soft-X-ray extensions of the big bump without exceeding the Eddington limit strongly. For a wide range of disk parameters, the EUV spectra of quasar disks should have spectral slopes near -1.

Czerny, Bozena↗

NASA NTRS1989

Disk-instability model for soft-X-ray transients containing black holes

Consideration is given to the time-dependent behavior of the accretion disks in low-mass X-ray binaries as a model for soft X-ray transients. The thermal stability and vertical structure properties of the disk are studied in the range between 10 to the 7th and 10 to the 8th cm. An Eulerian time-dependent thin disk model is used to show that, for relevant accretion rates, the disk suffers a thermal instability leading to intermittent accretion onto the central compact object. The disk instability model reproduces the basic features of outbursts of soft X-ray transients. Also, the physical state of quiescence of the binary A0620-00 is examined, focusing on the possible existence of a black hole. It is suggested that the modulation of the accretion flow in the inner disk may be responsible for the bimodal behavior observed in the spectra of black hole candidates such as Cyg X-1, GX 339-4, and A0620-00.

Mineshige, Shin↗

NASA NTRS1989

A study of the effects of disk flexibility on the rotordynamics of the space shuttle main engine turbo-pumps

Rotor dynamical analyses are typically performed using rigid disk models. Studies of rotor models in which the effects of disk flexibility were included indicate that is may be an important effect for many systems. This issue is addressed with respect to the Space Shuttle Main Engine high pressure turbo-pumps. Finite element analyses have been performed for a simplified free-free flexible disk rotor model and the modes and frequencies compared to those of a rigid disk model. The simple model was then extended to a more sophisticated HPTOP rotor model and similar results were observed. Equations were developed that are suitable for modifying the current rotordynamical analysis program to account for disk flexibility. Some conclusions are drawn from the results of this work as to the importance of disk flexibility on the HPTOP rotordynamics and some recommendations are given for follow-up research in this area.

Flowers, George T.↗

NASA NTRS1990

Self-collimated electromagnetic jets from magnetized accretion disks - The even-symmetry case

This paper extends the previous treatment (Lovelace et al., 1987) of the origin of self-collimated EM jets to the case of even field symmetry, where the magnetic flux function Psi(r, z) is an even function of z. A viscous resistive accretion disk is assumed to surround a black hole with a force-free plasma outside of the disk. Inside the disk, the induction equation is solved for Psi(r, z) and the toroidal magnetic field. Outside the disk, previous results are used to study the formation of self-collimated EM jets. In contrast with the odd-symmetry case, for even symmetry the toroidal magnetic field acts to vertically compress the disk; a comparatively large toroidal magnetic field can exist inside the disk; and an appreciable fraction (possibly all) of the available accretion power can go into the jets.

Wang, J. C. L.↗

NASA NTRS1990

A simple analytic model for the evolution of captured galactic disks

The general analytic solution developed by Steinman-Cameron and Durisen and published in 1988 for the evolution of dissipative nonplanar disks is applied to captured galactic disks in model galaxies with nonspherical, scale-free, logarithmic gravitational potentials. Such potentials produce flat rotation curves, similar to those seen in real galaxies. In this case, the analytic solution yields a self-similar structure for the warps and twists that develop while the disks is settling. Being scale-free in a simple, analytic form, this solution is completely defined by only a few dimensionless fitting parameters. As a result, it can be utilized as a mathematical tool to fit settling disks in real galaxies. The minimum time it takes for a disk to settle into a steady state orientation is also a scale-free quantity when expressed in units of the precession period or the orbit period. For realistic parameters, settling times are on the order of one-half to two periods. The use of the time-dependent structure of settling disks as a probe of the three-dimensional mass distribution of the host galaxies, including dark halos, is discussed.

Steiman-Cameron, Thomas Y.↗

NASA NTRS1990

Disk mass densities in edge-on spiral galaxies

Very Large Array (VLA) observations of the neutral hydrogen (HI) gas in two nearby edge-on spirals (NGC 4565 and NGC 891) successfully resolve the thickness of the gas layers in both disks over a wide range in radii. The combination of B, C, and D array data produces a 4 arcsec (approx. 200 pc) beam and 21 km s(exp -1) velocity resolution, combined with sensitivity to structures as large as 18 arcmin (approx. 54 kpc). These observations directly constrain the mid-plane disk mass densities, under the assumption of an equilibrium between the thermal pressure of the gas and the gravitational attraction of the disk. The results of a preliminary analysis are given regarding the z-velocity dispersion of the gas, the mass-to-light ratio of the disk in NGC 4565, and the roles of atomic and molecular gases. The data also allow a detailed study of the HI in these galaxies; in general their brightness temperature distributions seem similar to that in the Milky Way. Both galaxies show asymmetric HI extensions beyond the optical disk. In NGC 4565 the extension is a surprisingly abrupt warp, which may bend back to parallel the galactic plane; the velocity structure implies the warp is continuous around the disk.

Rupen, Michael P.↗

NASA NTRS1990

Stationary orbits of satellites of disk galaxies

The satellite of an S-galaxy will experience opposing dynamical-friction forces from the stars of the disk and the halo. If these forces are in balance, the satellite may travel in a stable, near-circular orbit whose radius, for a wide range of physical parameters, should be limited to a zone 1.2 to 1.4 times the disk radius, much as is observed. The idea is very simple. The dynamical friction acting on a small satellite, moving through a stellar galactic halo, makes this satellite slow down. On the other hand, a stellar disk, rotating faster than a satellite, makes it speed up. But the density distributions in radius for disk's and halo's stars in real flat galaxies are quite different (respectively, exponential and power-law). Moreover, the observational data show that the exponential profile for disk's surface density drops abruptly at some radius (r sub d). So it is natural to expect that a stationary orbit could be near the edge of a disk (where two effects are mutually compensated).

Polyachenko, Valerij L.↗

NASA NTRS1991

Formation and evolution of the protoplanetary disk

A disk formation model during collapse of the protosolar nebula, yielding a low-mass protoplanetary disk is presented. The following subject areas are covered: (1) circumstellar disks; (2) conditions for the formation of stars with disks; (3) early evolution of the protoplanetary disk; and (4) temperature conditions and the convection in the protoplanetary disk.

Ruzmaikina, Tamara V.↗

NASA NTRS1991

Accretion disk emission from a BL Lacertae object

It is suggested here that the UV and X-ray emission of BL Lac objects may originate in an accretion disk. Using detailed calculations of accretion disk spectra, the best-measured ultraviolet and soft X-ray spectra of the BL Lac object PKS 2155-304 are fitted, and the mass and accretion rate required is determined. The ultraviolet through soft X-ray continuum is well fitted by the spectrum of an accretion disk, but near-Eddington accretion rates are required to produce the soft X-ray excess. A hot disk or corona could Comptonize soft photons from the cool disk and produce the observed power-law spectrum in the 1-10 keV range. The dynamic time scale in the disk regions that contribute most of the observed ultraviolet and soft X-ray photons are consistent with the respective time scales for intensity variations observed in these two wave bands; the mass derived from fitting the continuum spectrum is consistent with the limit derived from the fastest hard X-ray variability.

Wandel, Amri↗

NASA NTRS1990

Nonlinear evolution of protostellar disks and light modulations in young stellar objects

An evolutionary model of dynamical processes in protostellar disks is described and illustrated with graphs of typical results. The effective transport mechanisms are discussed, including thermal convection, nonaxisymmetric gravitational instabilities in the outer regions of disks, and wave propagation. Consideration is then given to the stages of dynamical evolution, FU Ori outburst phenomena, unsteady accretion-disk flows, and nonlinear feedback as a mechanism to modulate mass transfer. The simulations show that mass redistribution is determined by angular-momentum transfer, which in turn is regulated by the effective viscosity generated by convectively driven turbulence. Significant mass transfer occurs as a result of mixing of infalling material with disk gas and is affected by the tidal torque associated with the growth of nonaxisymmetric disturbances in the outer disk. The time scale for disk evolution is found to be about 1 Myr.

Lin, D. N. C.↗

NASA NTRS1990

The flow of a thin liquid film on a stationary and rotating disk. I - Experimental analysis and flow visualization

The mean thickness of a thin liquid film of deionized water with a free surface on a stationary and rotating horizontal disk has been measured with a nonobtrusive capacitance technique. The measurements were taken when the rotational speed was 0-300 RPM and the flow rate was 7.0-15.0 LPM. A flow visualization study of the thin film was also performed to determine the characteristics of the waves on the free surface. When the disk was stationary, a circular hydraulic jump was present on the disk. Surface waves were found in the supercritical and subcritical regions at all flow rates studied. When the rotational speed of the disk is low, a standing wave at the edge of the disk was present. As the rotational speed increased, the surface waves changed from the wavy-laminar region to a region in which the waves ran nearly radially across the disk on top of a thin substrate of fluid.

Thomas, S.↗

NASA NTRS1991

Can a disk model explain Beta Lyrae?

The Beta Lyrae eclipsing binary system is interpreted in terms of a model where the primary, i.e., spectroscopically observable, B star transfers matter to a 'canonical' accretion disk surrounding a 'gainer' which may be a rather ordinary B0.5 V star. Disk models are calculated using the TLUSDISK program. Most of the optical radiation from the secondary object is found to come from the disk rim, provided that the rate of mass transfer is not much lower than about 0.0001 solar mass per year. The rather high disk rim then introduces severe constraints on the orbital inclination; these constraints are discussed in detail. It is concluded that the disk plays an essentially passive role, and the observable radiation from its face is insignificant. A model in which most ultraviolet radiation would be coming from the face of the disk is found unacceptable both because of these constraints and because it would require an unrealistically small radius for the accreting star. It is proposed that the bulk of the ultraviolet radiation comes from a small unocculted segment of the gainer.

Hubeny, Ivan↗

NASA NTRS1991

Dynamo magnetic-field generation in turbulent accretion disks

Magnetic fields can play important roles in the dynamics and evolution of accretion disks. The presence of strong differential rotation and vertical density gradients in turbulent disks allows the alpha-omega dynamo mechanism to offset the turbulent dissipation and maintain strong magnetic fields. It is found that MHD dynamo magnetic-field normal modes in an accretion disk are highly localized to restricted regions of a disk. Implications for the character of real, dynamically constrained magnetic fields in accretion disks are discussed. The magnetic stress due to the mean magnetic field is found to be of the order of a viscous stress. The dominant stress, however, is likely to come from small-scale fluctuating magnetic fields. These fields may also give rise to energetic flares above the disk surface, providing a possible explanation for the highly variable hard X-ray emission from objects like Cyg X-l.

Stepinski, T. F.↗